Classes Of Life Distributions Research Articles

Advancements in Laplace transform techniques: Performing non-parametric hypothesis testing on real-world data through statistical analysis

This research delves into the exploration of a statistical testing approach grounded in Laplace transform techniques specifically tailored for the New Better than Used Laplace transform order (NBUL) class of life distributions. The developed test exhibits versatility, accommodating both complete and censored data, and critical values are systematically calculated for its application. Beyond the methodological presentation, our study investigates the test’s statistical power and explores Pitman’s asymptotic efficiency concerning various alternative distributions. Comparative analyses with other tests within the same class contribute to a comprehensive understanding of the proposed approach. To demonstrate practical applicability, we apply this novel testing technique to authentic engineering and medical datasets. The outcomes of these applications serve as illustrative examples, showcasing the effectiveness and relevance of the proposed methodology in real-world scenarios.

Statistical Insights: Analyzing Shock Models, Reliability Operations and Testing Exponentiality for NBRUmgf Class of Life Distributions

This study deals with a novel category of life distributions called the new better than renewal used in moment generating function (NBRUmgf) class. It delves into the connections between this form of aging and established aging categories, along with its relevance in a shock model. Additionally, it explores how this aging concept remains consistent through certain reliability operations which is consider a very important tool in reliability engineering. The research computes Pitman's asymptotic efficiencies for this testing procedure, comparing them with alternative methods. Furthermore, the study furnishes a comprehensive table of percentiles for the test statistic associated with this proposed method. Furthermore, in order to showcase the relevance of the study's conclusions, we utilize distinct real-world datasets, which illustrate the effectiveness of our test across various types of real data.

Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored δ Shock Model

A fresh censored δ shock model is investigated. The arrival of random shocks follows a generalized Pólya process, and the failure mechanism of the system occurs based on the censored δ shock model. The generalized Pólya process is used for modeling because the generalized Pólya process has excellent properties, including the homogeneous Poisson process, the non-homogeneous Poisson process, and the Pólya process. Thus far, the lifetime properties of the censored δ shock model under the generalized Pólya process have not been studied. Therefore, for the established generalized Pólya censored δ shock model, the corresponding reliability function, the upper bound of the reliability function, the mean lifetime, the failure rate, and the class of life distribution are obtained. In addition, a replacement strategy N, based on the number of failures of the system, is considered using a geometric process. We determined the optimal replacement policy N* by objective function minimization. Finally, a numerical example is presented to verify the rationality of the model.

A new non-parametric hypothesis testing with reliability analysis applications to model some real data

Due to the essential necessities of current technology and contemporary sciences, a methodical approach to investigating every occurrence or action occurring in the world was required. As a result, it makes sense that such an approach would be required in the investigation of the reliability of technological systems and products. In actuality, there are instances when system parts gradually deteriorate over time t, at which point the system needs to be updated by replacing the spare parts. Although renewal tries to improve system usability, it is unable to restore the system to its prior state. We discovered that an entirely novel domain of reliability known as classes of life distributions has emerged as a result of the growth of criteria for determining the success or failure of dependability over the previous few decades. Moreover, the other nonparametric tests of life distribution lack test efficiency and have low test power. On the other hand, based on that approach, the non-parametric statistical test utilized in this study evaluates different types of treatment by examining failure behavior in the survival data that was collected. As a result, in this ivestigation, we have developed a novel test of life distribution in this study that considers the power and effectiveness of the test. In order to compare data belonging to the harmonic new better than used in expectation (HNBUE) class with data that follow an exponential distribution, this article suggests nonparametric tests for both censored and uncensored data. The higher percentile points of the test statistics are collected, and the suggested test's normality is verified. The Pitman asymptotic relative efficiency (PARE) and powers of proposed test are calculated a few well-known alternative asymmetric models. Three asymmetric real-world data sets are examined to demonstrate the paper's findings.

Dynamic cumulative residual entropy generating function and its properties

In this work, we study the properties of the cumulative residual entropy generating function (CREGF). We also discuss the non parametric estimation of CREGF. We introduce dynamic cumulative residual entropy generating function (DCREGF). It is shown that the DCREGF determines the distribution uniquely. We study some characterization results using the relationship between DCREGF, hazard rate, and mean residual life function. A new class of life distributions based on decreasing DCREGF is introduced. Finally, we develop a test for decreasing DCREGF and study its performance.

Non-Parametric Hypothesis Testing for Unknown Aged Class of Life Distribution Using Real Medical Data

Over the last few decades, the statisticians and reliability analysts have looked at putting exponentiality to the test using the Laplace transform technique. The non-parametric statistical test used in this study, which is based on this technique, evaluates various treatment modalities by looking at failure behavior in the survival data that were gathered. Following use of the suggested strategy, patient survival times are recorded. In this investigation, it was presupposed that the Laplace transform order of (UBAC2) attribute or the constant failure rate would determine how the observed data behave (exponential scenario). If the survival data are exponential, the recommended treatment approach is ineffective. If the survival data are UBAC2L, the technique in use produces a better or a higher expected total present value than an older one governed by an exponential survival function (discussed in the Applications section). The efficiency and critical values of the test are calculated and compared to those of other tests in order to ensure that the suggested statistical test is applied correctly.

A New Reliability Class-Test Statistic for Life Distributions under Convolution, Mixture and Homogeneous Shock Model: Characterizations and Applications in Engineering and Medical Fields

Over the past few decades, a new area of reliability known as classes of life distributions has developed as a result of the creation of metrics for evaluating the success or failure of reliability. This paper proposes a new reliability class-test statistic for life distributions. In some reliability processes, such as convolution, mixture, and homogeneous shock models, the closure characteristics of the proposed class-test statistic are investigated. To compare the proposed class-test against some competitive tests, the Weibull, linear failure rate (LFR), and Makeham distributions are evaluated. In addition, the relationship between sample size, level of confidence, and critical values is considered to assess the efficacy of the proposed class-test. Furthermore, a Monte Carlo null distribution critical points simulation and some applications of the censored and uncensored data are performed to demonstrate the validity of the proposed class-test in reliability analysis.

Discrete Mean Inactivity Time Function, Associated Orderings, and Classes of Life Distributions

Discrete Mean Inactivity Time Function, Associated Orderings, and Classes of Life Distributions

Characterizations and Testing Hypotheses for NBRUL-t $$_{0}$$ Class of Life Distributions

Characterizations and Testing Hypotheses for NBRUL-t $$_{0}$$ Class of Life Distributions

Reliability Analysis of the Inverse Modified Weibull Model with Applications

This paper presents a novel flexible inverse modified Weibull model with a concave Weibull probability diagram that describes various reliability phenomena. We investigate some essential attributes and reliability properties of this model. The new model exhibits an increasing or unimodal form of the hazard rate function, making it more suitable for simulating certain aging classes of life distributions with appropriate choices of parameter values. We used the Weibull probability paper approach and the maximum likelihood method to estimate the model's parameters. In addition, we conduct a simulation study to investigate the behavior and efficiency of these estimators. Finally, we analyze a maintenance dataset to demonstrate the usefulness of the proposed model.

Nonparametric Test for a class of Lifetime Distribution UBAC(2) Based on the Laplace Transform

Testing various classes of life distributions have been considered a very important problem in the literature during the last decades, and many authors tried to solve it. In this paper, a new statistic technique for testing exponentiality versus the class of life distribution used better than aged in increasing concave ordering (UBAC(2)) is introduced based on the Laplace transform. For this proposed test, the critical values, the pitman’s asymptotic efficiency and the power of the test are calculated via simulation to assess the performance of the test. A new nonparametric test statistic for testing exponentiality versus UBAC(2) for right censored data is proposed, and the critical values are tabulated. Finally, real data are used for complete and censored data by using our proposed test.

A New Class of Life Distribution based on Laplace Transform and It’s Applications

A New Class of Life Distribution based on Laplace Transform and It’s Applications

Characterizations and Testing NBRUL Class of Life Distributions Based on Laplace Transform Technique

Characterizations and Testing NBRUL Class of Life Distributions Based on Laplace Transform Technique

A New Class of Life Distributions Based on Moment Inequalities

In this paper, a new class of life distribution is named new better than renewal used in moment generating function (NBRUmgf). A new test for exponentiality versus NBRUmgf based on moment inequalities is established. Pitman's asymptotic efficiencies, powers and critical values of the new test are calculated to assess the performance of the test. The right censored data is handled also. Finally some applications are applied to the new test.

On classes of life distributions based on the mean time to failure function

AbstractThe performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. We develop shock model theory in different scenarios for classes of life distributions based on the MTTF function where the probabilities $\bar{P}_k$ of surviving the first k shocks are assumed to have discrete DMTTF, IMTTF and IDMTTF properties. The cumulative damage model of A-Hameed and Proschan [1] is studied in this context and analogous results are established. Weak convergence and moment convergence issues within the IDMTTF class of life distributions are explored. The preservation of the IDMTTF property under some basic reliability operations is also investigated. Finally we show that the intersection of IDMRL and IDMTTF classes contains the BFR family and establish results outlining the positions of various non-monotonic ageing classes in the hierarchy.

Some New Bounds for Moment Generating Functions of Various Life Distributions Using Mean Residual Life Functions

In this paper, we present bounds for moment generating functions of certain life distributions, including the decreasing mean residual life class. We also give bounds for some other much larger classes of life distributions. Most bounds are based on the mean residual life functions. These bounds are compared to some other bounds in the literature. The methods used can also find bounds for other functions of the lifetime random variable. Some applications to bounding tail probabilities of lifetime distributions are given.

Testing of UBAC(2) Class of Life Distributions based on TTT - Transform

Testing of UBAC(2) Class of Life Distributions based on TTT - Transform

Nonparametric Testing for Unknown Age (UBAL) Class of Life Distribution

Abstract In this article, a test statistic for testing exponentiality versus a used better than aged in Laplace transform ordering class of life distribution based on a U-statistic is proposed. Pitman’s asymptotic efficiencies of the test are calculated and compared to other tests. The percentiles of this test statistic are tabulated for censored and non-censored data, and the powers of this test are estimated for some famously alternative distributions in reliability, such as the Weibull, Makeham, linear failure rate, and Gamma distributions. Finally, examples in different areas are used as practical applications of the proposed test.

A New Nonparametric Class of Life Distributions Based on Ordering Moment Generating Approach

A New Nonparametric Class of Life Distributions Based on Ordering Moment Generating Approach

Stochastic comparisons and ageing properties of RLRT (ITRT) based on variance residual life

Stochastic comparisons and ageing properties of residual life (inactivity time) of a random variable X at random time Y (RLRT/ITRT) taking X and Y independent have been investigated in the literature. In this article, we consider X and Y not necessarily independent and obtain stochastic comparison results for RLRT and ITRT based on variance residual life (VRL) order. We also study various ageing properties of RLRT/ITRT based on the associated classes of life distributions of VRL. An application of one of the results derived in this paper is also illustrated.